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The game uses a 3x3 square board. 2 players take turns to play,
either placing a red on an empty square, or changing a red to
orange, or orange to green. The player who forms 3 of 1 colour in a
line wins.

Some puzzles requiring no knowledge of knot theory, just a careful
inspection of the patterns. A glimpse of the classification of
knots and a little about prime knots, crossing numbers and knot
arithmetic.

Dicey Operations

Stage: 2 and 3 Challenge Level:

Find a partner and a 1-6 dice, or preferably a 0-9 dice if you have one. The interactivity in Dice and Spinners can be used to simulate throwing different dice.

Take turns to throw the dice and decide which of your cells to fill.
This can be done in two ways: either fill in each cell as you throw the dice, or collect all your numbers and then decide where to place them.

Game 1

Each of you draw an addition grid like this:

Throw the dice nine times each until all the cells are full.

Whoever has the sum closest to 1000 wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 1000 after each round. First to 5000 loses.

You can vary the target to make it easier or more difficult.

Game 2

Each of you draw a subtraction grid like this:

Throw the dice eight times each until all the cells are full.

Whoever has the difference closest to 1000 wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 1000 after each round. First to 5000 loses.

You can vary the target to make it easier or more difficult, perhaps including negative numbers as your target.

Game 3

Each of you draw a multiplication grid like this:

Throw the dice four times each until all the cells are full.

Whoever has the product closest to 1000 wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 1000 after each round. First to 5000 loses.

You can vary the target to make it easier or more difficult.

Game 4

Each of you draw a multiplication grid like this:

Throw the dice five times each until all the cells are full.

Whoever has the product closest to 10000 wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 10000 after each round. First to 10000 loses.

You can vary the target to make it easier or more difficult.

You could introduce a decimal point. The decimal point could take up one of the cells so the dice would only need to be thrown four times by each player. You will need to decide on an appropriate target.

Game 5

Each of you draw a division grid like this:

Throw the dice five times each until all the cells are full.

Whoever has the answer closest to 1000 wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 1000 after each round. First to 5000 loses.

You can vary the target to make it easier or more difficult.

Game 6

Each of you draw a division grid like this:

Throw the dice six times each until all the cells are full.

Whoever has the answer closest to 100 wins.

There are two possible scoring systems:

A point for a win. The first person to reach 10 wins the game.

Each player keeps a running total of their "penalty points", the difference between their result and 100 after each round. First to 500 loses.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.